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Tables of Contents for Statistical Mechanics
Chapter/Section Title
Page #
Page Count
Editor's Foreword
v
6
Acknowledgments
xi
Chapter 1 Introduction to Statistical Mechanics
1
38
1.1 The Partition Function
1
38
Chapter 2 Density Matrices
39
33
2.1 Introduction to Density Matrices
39
5
2.2 Additional Properties of the Density Matrix
44
3
2.3 Density Matrix in Statistical Mechanics
47
1
2.4 Density Matrix for a One-Dimensional Free Particle
48
1
2.5 Linear Harmonic Oscillator
49
4
2.6 Anharmonic Oscillator
53
5
2.7 Wigner's Function
58
2
2.8 Symmetrized Density Matrix for N Particles
60
4
2.9 Density Submatrix
64
2
2.10 Perturbation Expansion of the Density Matrix
66
1
2.11 Proof that F is less than or equal to Fo + [H - Ho]o
67
5
Chapter 3 Path Integrals
72
25
3.1 Path Integral Formation of the Density Matrix
72
6
3.2 Calculation of Path Integrals
78
6
3.3 Path Integrals by Perturbation Expansion
84
2
3.4 Variational Principle for the Path Integral
86
2
3.5 An Application of the Variation Theorem
88
9
Chapter 4 Classical System of N Particles
97
30
4.1 Introduction
97
3
4.2 The Second Virial Coefficient
100
5
4.3 Mayer Cluster Expansion
105
6
4.4 Radial Distribution Function
111
2
4.5 Thermodynamic Functions
113
2
4.6 The Born-Green Equation for n(2)
115
2
4.7 One-Dimensional Gas
117
3
4.8 One-Dimensional Gas with Potential of the Form e^(-|x|)
120
5
4.9 Brief Discussion of Condensation
125
2
Chapter 5 Order-Disorder Theory
127
24
5.1 Introduction
127
3
5.2 Order-Disorder in One-Dimension
130
1
5.3 Approximate Methods for Two Dimensions
131
5
5.4 The Onsager Problem
136
13
5.5 Miscellaneous Comments
149
2
Chapter 6 Creation and Annihilation Operators
151
47
6.1 A Simple Mathematical Problem
151
3
6.2 The Linear Harmonic Oscillator
154
2
6.3 An Anharmonic Oscillator
156
1
6.4 Systems of Harmonic Oscillators
157
2
6.5 Phonons
159
3
6.6 Field Quantization
162
5
6.7 Systems of Indistinguishable Particles
167
9
6.8 The Hamiltonian and Other Operators
176
7
6.9 Ground State for a Fermion System
183
2
6.10 Hamiltonian for a Phonon-Electron System
185
5
6.11 Photon-Electron Interactions
190
2
6.12 Feynman Diagrams
192
6
Chapter 7 Spin Waves
198
23
7.1 Spin-Spin Interactions
198
2
7.2 The Pauli Spin Algebra
200
2
7.3 Spin Wave in a Lattice
202
4
7.4 Semiclassical Interpretation of Spin Wave
206
1
7.5 Two Spin Waves
207
2
7.6 Two Spin Waves (Rigorous Treatment)
209
3
7.7 Scattering of Two Spin Waves
212
3
7.8 Non-Orthogonality
215
2
7.9 Operator Method
217
1
7.10 Scattering of Spin Waves-Oscillator Analog
218
3
Chapter 8 Polaron Problem
221
21
8.1 Introduction
221
4
8.2 Perturbation Treatment of the Polaron Problem
225
6
8.3 Formulation for the Variational Treatment
231
3
8.4 The Variational Treatment
234
7
8.5 Effective Mass
241
1
Chapter 9 Electron Gas in a Metal
242
23
9.1 Introduction: The State Function XXX
242
2
9.2 Sound Waves
244
2
9.3 Calculation of P(R)
246
2
9.4 Correlation Energy
248
1
9.5 Plasma Oscillation
249
3
9.6 Random Phase Approximation
252
2
9.7 Variational Approach
254
1
9.8 Correlation Energy and Feynman Diagrams
255
7
9.9 Higher-Order Perturbation
262
3
Chapter 10 Superconductivity
265
47
10.1 Experimental Results and Early Theory
265
4
10.2 Setting Up the Hamiltonian
269
4
10.3 A Helpful Theorem
273
1
10.4 Ground State of a Superconductor
274
3
10.5 Ground State of a Superconductor (continued)
277
2
10.6 Excitations
279
2
10.7 Finite Temperatures
281
4
10.8 Real Test of Existence of Pair States and Energy Gap
285
5
10.9 Superconductor with Current
290
3
10.10 Current Versus Field
293
5
10.11 Current at a Finite Temperature
298
5
10.12 Another Point of View
303
9
Chapter 11 Superfluidity
312
39
11.1 Introduction: Nature of Transition
312
7
11.2 Superfluidity--An Early Approach
319
2
11.3 Intuitive Derivation of Wave Functions: Ground State
321
5
11.4 Phonons and Rotons
326
4
11.5 Rotons
330
4
11.6 Critical Velocity
334
1
11.7 Irrotational Superfluid Flow
335
2
11.8 Rotational of the Superfluid
337
2
11.9 A Reasoning Leading to Vortex Lines
339
4
11.10 The Lambda Transition in Liquid Helium
343
8
Index
351